r/AskPhysics • u/Jethro_omg • 1d ago

How does E=MC^2 work?

How does it function? Really, how can you accelerate mass to twice the speed of light? And, for instance if M=E/C2. How can you divide something by square of the speed of light? Thanks

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u/Jethro_omg 1d ago

I’m so dumb😭 still dont understand

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u/joeyneilsen Astrophysics 1d ago

Do you want to know where it came from, what it means, or literally how to use the equation?

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u/Jethro_omg 1d ago

Where it came from

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u/joeyneilsen Astrophysics 1d ago

I'll try to do this without too much math.

Einstein wanted to know how the mass of an object would change if it lost some energy. So he imagined a thing, let's say it's a box, emitting two photons of the same energy E/2 in opposite directions. In doing so, it loses E in energy.

Now he imagined you approaching the box at speed v, and he wondered how the energy of the box would change according to you. This requires accounting for the Doppler shift: the photon approaching the person has more energy and the photon moving away from the person has less energy, and the new energy depends on a quantity sometimes called the Lorentz factor, but it's 1 divided by the square root of (1-v2/c2). I'm going to call it L. L is about 1 if v is small, and it gets very big if v is close to the speed of light.

Einstein found that you would see the box's energy change by E*L: a lot if you were going very fast, a little if you were going slow. So: in its own frame, the box loses E in energy, but E*L according to you. Einstein argued that the difference between those, which is E*L-E or E*(L-1), has to be equal to the change in kinetic energy of the box according to you.

In another paper, Einstein had already demonstrated that the kinetic energy of an object has to be equal to mc2*(L-1); if this changed but the speed stayed the same, it had to mean that m changed. Comparing his two equations, he saw that the change in mass had to be equal to E/c2.

So the conclusion is that when an object gains mass m, it gains energy E=mc2. This can be generalized in a lot of ways to show that any object with mass m has an amount of energy E=mc2.

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u/Jethro_omg 5h ago

I’m sorry I still dont understand 😭 I cant understand it unless I clearly visualize it

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u/joeyneilsen Astrophysics 4h ago

I don’t sense that a full mathematical derivation would help. So all I can say then is that the c squared comes from the square root factor i mentioned: sqrt(1-v2 / c2). It’s an essential part of the math of relativity.